Identifiability of an X-Rank Decomposition of Polynomial Maps

Pierre Comon 1 Yang Qi 2 Konstantin Usevich 1
1 GIPSA-CICS - CICS
GIPSA-DIS - Département Images et Signal
Abstract : In this paper, we study a polynomial decomposition model that arises in problems of system identification, signal processing and machine learning. We show that this decomposition is a special case of the X-rank decomposition --- a powerful novel concept in algebraic geometry that generalizes the tensor CP decomposition. We prove new results on generic/maximal rank and on identifiability of a particular polynomial decomposition model. In the paper, we try to make results and basic tools accessible for general audience (assuming no knowledge of algebraic geometry or its prerequisites).
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Contributor : Pierre Comon <>
Submitted on : Wednesday, April 11, 2018 - 2:48:00 PM
Last modification on : Monday, November 26, 2018 - 5:04:03 PM

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Pierre Comon, Yang Qi, Konstantin Usevich. Identifiability of an X-Rank Decomposition of Polynomial Maps. SIAM Journal on Applied Algebra and Geometry, SIAM, 2017, 1 (1), pp.388 - 414. ⟨https://epubs.siam.org/toc/sjaabq/1/1⟩. ⟨10.1137/16M1108388⟩. ⟨hal-01763858⟩

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